Details

analyze213.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
373×	`neg-mul-1_binary64` `neg-sub0_binary64`
340×	`+-commutative_binary64`
277×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	61	46
2	152	46
3	438	46
4	1297	46
5	2510	46
6	4609	46
7	5033	46

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 99 to 63 computations (36.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite205.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3111 to 1674 computations (46.2% saved)

series224.0ms (4.2%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

85.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
53.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
26.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
14.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 3053 to 2263 computations (25.9% saved)

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

853×	`distribute-rgt-in_binary64`
794×	`distribute-lft-in_binary64`
274×	`cancel-sign-sub-inv_binary64`
246×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

133 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3004
1	533	2684
2	1756	2599
3	5455	2599

prune113.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Error

Counts

106 → 4

Alt Table

Status	Error	Program
	0.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (+.f64 (.f64 a a) (pow.f64 a 3)))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (+.f64 (.f64 a a) (pow.f64 a 3))))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (+.f64 (*.f64 a a) (pow.f64 a 3))))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
	11.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 2528 to 1418 computations (43.9% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1)))) (pow.f64 a 4))
0.0b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
0.1b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
0.8b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))

rewrite274.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-log-exp_binary64`
14×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64` `associate-*r/_binary64`
7×	`sum-log_binary64`
6×	`pow-prod-down_binary64` `prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `-un-lft-identity_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-r*_binary64`

Counts

4 → 83

Calls

4 calls:

19.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
13.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1)))) (pow.f64 a 4))
11.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))
7.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 4438 to 2844 computations (35.9% saved)

series288.0ms (5.4%)

Error

Counts

4 → 56

Calls

4 calls:

85.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
73.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1)))) (pow.f64 a 4))
49.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))
29.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 3495 to 2731 computations (21.9% saved)

simplify193.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

501×	`cancel-sign-sub-inv_binary64`
396×	`associate-l_binary64`
356×	`associate-r_binary64`
252×	`distribute-rgt-neg-in_binary64`
226×	`distribute-rgt-in_binary64`

Counts

139 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4842
1	772	4515
2	3139	4497
3	4977	4497
4	4995	4497
5	4930	4497

prune162.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Error

Counts

114 → 4

Alt Table

Status	Error	Program
▶	9.1b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (cbrt.f64 (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))) 3)))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
	11.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 3387 to 2228 computations (34.2% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
0.2b	(pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))) 3)
3.3b	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4)))) 3))
24.2b	(cbrt.f64 (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4)))) 3)))

rewrite283.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
16×	`unpow-prod-down_binary64`
15×	`associate-r_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `unswap-sqr_binary64`

Counts

4 → 112

Calls

4 calls:

17.0ms	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4)))) 3))
13.0ms	(cbrt.f64 (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4)))) 3)))
11.0ms	(pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))) 3)
7.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 4987 to 3290 computations (34% saved)

series384.0ms (7.2%)

Error

Counts

4 → 67

Calls

4 calls:

112.0ms	(.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4)))) 3))
85.0ms	(pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))) 3)
60.0ms	(cbrt.f64 (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4)))) 3)))
31.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 6556 to 5142 computations (21.6% saved)

simplify129.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-+r+_binary64`
547×	`associate-r_binary64`
511×	`associate-l_binary64`
382×	`associate-+l+_binary64`
158×	`+-commutative_binary64`

Counts

179 → 144

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	405	7297
1	1156	6397
2	5258	6397

prune217.0ms (4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
✓	9.1b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (cbrt.f64 (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))) 3)))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
▶	11.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 4978 to 3430 computations (31.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
23.2b	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))

rewrite176.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64` `associate-r_binary64`

Counts

4 → 81

Calls

4 calls:

8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))

Compiler

Compiled 2996 to 1640 computations (45.3% saved)

series141.0ms (2.6%)

Error

Counts

4 → 38

Calls

4 calls:

52.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))
27.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
22.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
14.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2504 to 1793 computations (28.4% saved)

simplify135.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

431×	`distribute-rgt-in_binary64`
405×	`exp-prod_binary64`
387×	`distribute-lft-in_binary64`
344×	`*-commutative_binary64`
269×	`log-prod_binary64`

Counts

119 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	158	1912
1	373	1726
2	1150	1695
3	2777	1659
4	4322	1608
5	4954	1608
6	4990	1608

prune90.0ms (1.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
	9.1b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (cbrt.f64 (.f64 (pow.f64 a 6) (pow.f64 (+.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))) 3)))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
	11.6b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 1826 to 1031 computations (43.5% saved)

regimes970.0ms (18.1%)

Accuracy

Total 0.0b remaining (62.8%)

Threshold costs 0.0b (62.8%)

Compiler

Compiled 22749 to 15487 computations (31.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`1-exp_binary64` `distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	61
1	48	61
2	58	61
3	62	61
4	64	61
5	61	61

end1.0ms (0%)

Compiler: Compiled 43 to 34 computations (20.9% saved)

sample903.0ms (16.8%)

Algorithm

1×

intervals

Results

503.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 223 to 156 computations (30% saved)

Details

analyze213.0ms (4%)

sample27.0ms (0.5%)

simplify61.0ms (1.1%)

prune4.0ms (0.1%)

localize16.0ms (0.3%)

rewrite205.0ms (3.8%)

series224.0ms (4.2%)

simplify87.0ms (1.6%)

prune113.0ms (2.1%)

localize20.0ms (0.4%)

rewrite274.0ms (5.1%)

series288.0ms (5.4%)

simplify193.0ms (3.6%)

prune162.0ms (3%)

localize25.0ms (0.5%)

rewrite283.0ms (5.3%)

series384.0ms (7.2%)

simplify129.0ms (2.4%)

prune217.0ms (4%)

localize17.0ms (0.3%)

rewrite176.0ms (3.3%)

series141.0ms (2.6%)

simplify135.0ms (2.5%)

prune90.0ms (1.7%)

regimes970.0ms (18.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample903.0ms (16.8%)

Profiling